Computing Periods\(\ldots \)

Abstract

A period is the difference between the volumes of two semi-algebraic sets. Recent research has located their worst-case complexity in low levels of the Grzegorczyk Hierarchy. The present work introduces, analyzes, and evaluates three rigorous algorithms for rigorously computing periods: a deterministic, a randomized, and a ‘transcendental’ one.

Keywords

Based on ideas presented at CCA 2017, this work was supported by the National Research Foundation of Korea (grant NRF-2017R1E1A1A03071032) and the International Research & Development Program of the Korean Ministry of Science and ICT (grant NRF-2016K1A3A7A03950702). We thank the anonymous referees for feedback!